Penny Auctions

Penny Auctions &
Buy it Now
Gabi Lewis & Jason Lee
What are Penny Auctions?
“Win an Ipad for $40!”
Auction Format
• Bid packages, bid fees, price increments, timer.
Auction or Lottery?
Winner usually pays far less than value.
Loser can pay more than a winner.
Many lawsuits.
Exploit behavioral biases.
“Diabolically inventive” – Richard Thaler
Market Size
• May 2011: 8.46m unique visitors to all penny auction sites; 3.35m to Quibids.
Quibids Worked
Bid Costs: $0.60
Price increment: $0.02
Total bids: 174078/2 = 87,039
Quibids revenue = 87,039 x 0.60
= 52,223.40
Quibids profit = 52,223.40 20,000 = 32,223.40
Penny Auction Mechanics
• Auction format
• No bidding fee = First-Price Ascending
• No price increment = War of Attrition
• Unpredictable outcomes in real life.
• “Thrill of the hunt” and “Joy for bidding”.
• Sunk cost fallacy.
The Literature
Unexplored in the economics literature with a few exceptions:
• Platt, Price and Tappen (2011)
• Model suggests a distribution of ending prices (fitting with 57% of auctions).
• Augenblick (2011)
• Sunk costs explain bidder behavior and seller profits.
• Hinnosaar (2010)
• High variance of outcomes is a general property of penny auctions.
• Byers, Mitzenmacher and Zervas (2010)
• Analyze information asymmetry in response to models predicting zero seller profit.
Of all the auction formats studied extensively in the literature, most closely
resembles the dollar auction (Shubik 1971).
• Paradox of non-cooperation and escalation.
Models from Literature
• N players, fixed valuations, cost per bid.
• Set rounds (not representative of real auctions).
Continuous bidding or timer model.
• Almost no information asymmetries in terms of
number of players, bid costs, individual valuations
• Aggression model is non-existent with the exception
of most recent paper which looks at winning
statistics where:
• Aggression = # of Bids / Avg. Response Time
Objective / Problem
• Current models are too simple to capture bidding
• Most models find that buyers should simply purchase at
retail price
• Few models include the “Buy it Now” option and
none analyze its strategic implications.
• Objective: Provide a model that explains the
strategic implications of the “Buy it Now” option.
Buy it Now
• When the auction is over, participants can use previously made
bids as a credit towards purchasing the item at full price.
• Effects?
• Participants can recover their sunk costs.
• No naïve sunk cost fallacy.
• Less overbidding in attempts to recapture sunk investments.
• Upper bound on the potential loss of a participant.
• Increased participation.
• Aggression as a signaling mechanism becomes more credible.
• Hypothesis:
• Buy it Now  upper bound on potential loss  Chicken
The Model
Assume fixed price auction with price of zero.
v = common value of item to all players.
p = Buy it Now price offered by penny auction site, p>v
B = total bid costs of a player.
Imagine 2 players, each committed to using buy it now option.
They will bid either until B = p-v (maximum possible loss) and then use buy it now, or until they
win the auction outright and obtain the item at some discount.
If both players follow this strategy, they both lose maximum p-v.
If one player backs down, she loses –B, and other player obtains the item at some discount, βv.
The Model (continued)
We can model this game theoretically, as a 2x2 matrix.
Back Off
Play until End
Back Off
-B, -B
-B, βv
Play until End
βv, -B
p-v, p-v
 2 NE in pure strategies.
One player commits to continuing until the end and the other player backs off.
 If P1 knows with certainty that P2 will play until end, P1’s BR is back off.
 Aggression is a natural signaling mechanism.
The aggression should be early, because it only makes sense to back off when B<p-v. Once B>p-v, the player is
indifferent between bidding or backing off because she is guaranteed to lose p-v.
Conclusions & Future
• In our simplified model, the introduction of a “Buy
it Now” option suggests increased aggression
through the upper bound it creates on potential
• Implications of “Buy it Now” for seller?
• Introduced to increase participation/profit or to ward
off lawsuits?
• Bidding strategy/aggression with n>2 committed
players? Ascending price auction with price > 0?
Anderson, C. K., & Odegaard, F. (2011). Retail Selling With All-Pay Auctions. In Review. 1-27.
Byers, J. W., Mitzenmacher, M., & Zervas, G. (2010). Information Asymmetries in Pay-Per-Bid Auctions.
In ACM Conference on Electronic Commerce, 1–12.
Gnutzmann, H. (2011). Pay-per-bid Auctions. In Review. 1-14.
Hinnosaar, T. (2010). Penny auctions. Working paper, available at:, accessed 2011-11-10
Mittal, S. (2010). Equilibrium Analysis of Generalized Penny Auctions. 1-17.
Augenblick, N. (2009). Consumer and Producer Behavior in the Market for Penny Auctions. 19-21.
Platt, B. C., Price, J. and Tappen, H. (2011). Pay-to-Bid Auctions. 1-13.
Shubik, M. (1971) The Dollar Auction Game: A Paradox in Non-cooperative behavior and Escalation. In
The Journal of Conflict Resolution Volume 15 Issue 1, 109-111

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